Ok I better not see anyone complaining when I aimlessly pick on plebeians and flame the crap out of them as I usually do ...because I tried to have an intellectual conversation and you all failed ...miserably ...to entertain me! Such tyros. Anyway, I'm done being a pedant. On to masturbation.

Our Calculus teacher never taught us how to derive log manually (same with the trigonometric functions - sine, cosine, tangent, cotangent, secant, cosecant). It was a magic thing you required a calculator to get. -_- Although our trigo teacher did teach us how to derive the circular functions manually so that excused him for that part... but log remains a mystery only computers get.

JakeBenson saidOk I better not see anyone complaining when I aimlessly pick on plebeians and flame the crap out of them as I usually do ...because I tried to have an intellectual conversation and you all failed ...miserably ...to entertain me! Such tyros. Anyway, I'm done being a pedant. On to masturbation.

Isn't masturbation done by the "common people" and a person who makes an excessive or inappropriate display of learning just thinks about masturbation?

Which would explain why the pedant is so tense and needs a really good anal penetration?

So log(base 10)28 = 1.447 (using a calculator), as 10 to the 1.447 power equals 28.

Is there a way to answer this example on just a sheet of paper and without a calculator? It's really hard to calculate powers for me as I'm not sure how they increments (sort of exponentially?)

um......GEEKS UNITE!

I don't know what kind of paper calculation you meant, but if you have some constants handy and know the expansion of log(e base), you pretty much can evaluate any logarithm numbers by hand; such as following:

finally0.30103 + 1 + 0.146334 = 1.447364 (if you go to 6th order, number is like 1.44707)the calculator gives 1.447158, which means there is a chance to converge to this number if higher oder terms >7 are used.

What a scenic route to get log(base 10)28 !! it sounds silly.Maybe the main takeaway is that the lograthrim can always be broken down to smaller numbers or known numbers to be manageable.

FlashDrive saidI don't know what kind of paper calculation you meant, but if you have some constants handy and know the expansion of log(e base), you pretty much can evaluate any logarithm numbers by hand; such as following:

finally0.30103 + 1 + 0.146334 = 1.447364 (if you go to 6th order, number is like 1.44707)the calculator gives 1.447158, which means there is a chance to converge to this number if higher oder terms >7 are used.

What a scenic route to get log(base 10)28 !! it sounds silly.Maybe the main takeaway is that the lograthrim can always be broken down to smaller numbers or known numbers to be manageable.

FlashDrive saidI don't know what kind of paper calculation you meant, but if you have some constants handy and know the expansion of log(e base), you pretty much can evaluate any logarithm numbers by hand; such as following:

finally0.30103 + 1 + 0.146334 = 1.447364 (if you go to 6th order, number is like 1.44707)the calculator gives 1.447158, which means there is a chance to converge to this number if higher oder terms >7 are used.

What a scenic route to get log(base 10)28 !! it sounds silly.Maybe the main takeaway is that the lograthrim can always be broken down to smaller numbers or known numbers to be manageable.

Jakebenson, you have my admiration for your inteligence to even ask such a question. Just for the fun of it, what the hell is a logarithm ? I was in business management for 30 years and never had a need for it. Can this knowledge of and use of a logarithm be of value in my everyday life? How is this knowledge put to use? What line of work uses this knowledge? Mathematicians? Scientists? Architects? I'm not trying to be a smart ass either, I'm trying to learn something.

I haven't done calculus in awhile but.. I think a Taylor Series could pull it off. I hated them though, but pretty sure you don't need a calculator...

realifedad - Logarithms are mostly just for hard core calculus and such... as you can probably tell. Something it can be used for is extremely large numbers, like distance between solar systems etc. Another common example would be pH levels.

pH = log ( 1 / # of hydrogen ions as expressed in moles )

10 ^ pH = 1 / # of hydrogen ions

so a pH of 4 (acidic)...

10 ^ 4 = 1 / # of hydrogen ions

# of hydrogen ions = 0.0001 moles (per unit volume)

This means that for every single digit different the pH, its a factor of 10 in the # of hydrogen ions. So most people dont care how many thousands of ions... they just want a scale to determine if something will burn their eyes out or not.

Logarithms are everywhere, man! The logarithm function is the inverse of the exponential function: If y grows exponentially with x, then x grows logarithmically with y. The Richter magnitude scale is logarithmic, as is the pH scale, as CrownRoyal points out. The logarithm also appears in nature, in the form of the logarithmic spiral.

The most familiar mathematical application of the logarithm is the slide rule, owing to the fact that the log of a product is the sum of the logs of the factors. This means that a multiplication task can be converted into an addition task. It is also the basis of the following punny joke:

Noah opens up the ark and lets all the animals out, telling them to "Go forth and multiply." He's closing the great doors of the ark when he notices that there are two snakes sitting in a dark corner.

So he says to them, "Didn't you hear me? You can go now. Go forth and multiply."

"We can't," said the snakes, "We're adders."

Noah thinks for a while, then grabs his saw and hammer and runs off into the forest, where he cuts down a tree. He saws and hammers and builds a small table. He carefully picks up the snakes and puts them on the table.

"Go forth and multiply!" he commands.

The snakes look at each other, and then at Noah. "We can't, we're adders".

"Yes", Noah replies, "but, even adders can multiply on a log table".

In college quantitative courses you'll see the logarithm frequently used as a device to simplify a problem involving multiplication. However, the logarithm also appears unexpectedly in some truly profound and beautiful results in pure mathematics, such as the prime number theorem, which asserts that if you randomly select a number in the vicinity of n, the probability is roughly 1/log n that you got yourself a prime. Also the law of the iterated logarithm is a remarkable result about fluctuations in a random walk. It sez: almost surely, the random walk will be bounded by, and will approach arbitrarily closely, a curve shaped like sqrt(2n log log n) -- infinitely often.

zotamorf62 saidLogarithms are everywhere, man! The logarithm function is the inverse of the exponential function: If y grows exponentially with x, then x grows logarithmically with y. The Richter magnitude scale is logarithmic, as is the pH scale, as CrownRoyal points out. The logarithm also appears in nature, in the form of the logarithmic spiral....

In college quantitative courses you'll see the logarithm frequently used as a device to simplify a problem involving multiplication. However, the logarithm also appears unexpectedly in some truly profound and beautiful results in pure mathematics, such as the prime number theorem, which asserts that if you randomly select a number in the vicinity of n, the probability is roughly 1/log n that you got yourself a prime. Also the law of the iterated logarithm is a remarkable result about fluctuations in a random walk. It sez: almost surely, the random walk will be bounded by, and will approach arbitrarily closely, a curve shaped like sqrt(2n log log n) -- infinitely often.

FlashDrive saidMaybe the main takeaway is that the lograthrim can always be broken down to smaller numbers or known numbers to be manageable.

FlashDrive has it right. However, the power series for log(1+x) converges relatively slowly. The name of the game is to reduce your problem to calculating log(1+x) for x as close to zero as possible; you'll get a good approximation in fewer terms. For example, you could write

log10(28 ) = log10(28/25) + log10(25) = log10(1.12) + 2 log10(5)

Dispatch the first term using the power series approximation. Look up the second term, or use log10(5) = 1 - log10(2).